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On the Nature of the Positronic Bond

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On the Nature of the Positronic Bond On the nature of the positronic bond Mohammad Goli1 and Shant Shahbazian2 1School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran, E-mail: [email protected] 2Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran, Iran, 19839, P.O. Box 19395-4716. Tel/Fax: 98-21-22431661, E-mail: [email protected] Abstract Recently it has been proposed that the positron, the anti-particle analog of the electron, is capable of forming an anti-matter bond in a composite system of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859–8864 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates that the electron exchange phenomenon is virtually non-existent between the two atoms and no electronic covalent bond is conceivable in between. On the other hand, it is demonstrated that the positron density enclosed in each atom is capable of stabilizing interactions with the electron density of the neighboring atom. This electrostatic interaction suffices to make the whole system bonded against all dissociation channels. Thus, the positron indeed acts like an anti-matter glue between the two atoms. Keywords: Positron, atoms in molecules; bond theory; topological analysis, exotic molecules 1 Introduction The chemistry of exotic species, i.e. molecules containing exotic elementary particles like positron or positively/negatively charged muons, has a venerable history,[1] and in recent years the fields of the muonic,[2,3] and the positronic,[4,5] chemistries became mature subdisciplines of the exotic chemistry. Particularly, understanding positron’s interaction with molecules and the concomitant positron-electron annihilation process are of great interest. Beyond the academic curiosity, the annihilation process is the basis of the Positron Emission Tomography as a powerful medicinal imaging technique.[6] Accordingly, a large body of experimental,[7–10] and theoretical and computational,[11–31] studies have been conducted recently on polyatomic and diatomic,[32–39] positronic species in order to trace the sticking site of the positron. These studies reveal that in general the positronic density is very diffuse and is not centered between bonds but behind the most electronegative atom of the molecule (the cases with two or more atoms with equal electronegativity are more complicated).[20] It is usually perceived that the positron does not participate directly in forming the chemical bonds. Only through the reorganization of electronic structure, which seems to be marginal in general, positron may indirectly affect the bonds between atoms. However, in some very simple positronic species like positronium hydride,[40–43] positronic water,[44,45] and di-positronium,[46–48] there are evidence that the positron is actively participating in bonding interactions. By the way, it is hard to contemplate these species as composed of discernable atoms in molecules, so their classification as molecules is ambivalent and the chemical nature of bonding in these species yet seems to be obscure. 2 With such background in mind, the recently published paper by Charry, Varella and Reyes (hereafter denoted as CVR) claiming the first unambiguous positronic bond is quite striking.[49] Armed with their newly developed ab initio code, LOWDIN,[50,51] which is capable of dealing with multi-component quantum systems, the authors solved Schrödinger’s equation for +−2 species. The potential energy surface was derived eH, 2 with sufficient accuracy in order to claim its stability relative to all possible channels of dissociation. Interestingly, by deriving the positron’s density and comparing it to the + + electronic density of some well-known species, e.g. H 2 and Li2 , the authors provided some evidence that the positron is the main bonding agent acting as a glue between the two hydride ions. Based on these findings, it seems reasonable to symbolize this species − + − as H,, e H . The fact that the positron’s density is maximum between the two hydrides was interpreted by CVR as a manifestation of a one-positron covalent bond. Our aim in this communication is to verify detailed nature of the proposed positronic bond. Results and discussion In order to consider the positronic bond we employ the recently developed multi- component quantum theory of atoms in molecules (MC-QTAIM),[52–59] which is an extended version of the QTAIM proposed originally by Bader and coworkers.[60] The MC-QTAIM is the only available chemical theory specially designed to deal with the bonding analysis of the exotic species. The MC-QTAIM analysis is done taking into the number density and property densities of all types of quantum particles (not just those of electrons’). Using ab initio derived multi-component wavefunction of an exotic species, through a well-defined and unique machinery, which is system-independent and automated, the MC-QTAIM analysis derives the AIM and their properties. These 3 properties may then be used to access the bonding modes of the AIM in the exotic molecule as has been previously done in the case of the positronic,[61–63] and the muonic,[64–68] species. Particularly, the previous MC-QTAIM analysis of the positronic species revealed that the positron is not capable of accumulating enough electrons around itself to form an independent atomic basin.[62] In all the considered species the positron retains in the basin of the most electronegative atom except from the case of cyanide anion,CN − , where the positron’s population was almost evenly distributed in both atomic basins.[62] In present analysis we employ the MC-QTAIM trying to reveal the detailed nature of the AIM structure as well as the bonding mode of . Let us first very briefly discuss the energetics and stability of where − + − CVRH considered,, e H this species at various multi-component ab initio levels. The used computational levels were the MC-HF, the MC-MP2 and the MC-CI, combined with the standard correlation consistent basis sets for both electrons and the positron (hereafter the first basis set in the parenthesis is for electrons and the second one is for the positron).[49,50] At the highest ab initio levels, i.e. MC-CISDTQ/(aug-cc-pVDZ/aug-cc- pVDZ) and MC-CISDTQ/(aug-cc-pVTZ/aug-cc-pVTZ), the computed binding energies (BEs) relative to dissociation to the positronium hydride and the hydride ion, were ~55 and ~66 kJ.mol-1, respectively.[49] We employed the same basis sets and the NEO computer code,[69,70] with some modifications, to compute BEs at the MC-HF level. At fixed 3.2 Å inter-nuclear distance, derived as the equilibrium point at the MC-CISDTQ level,[49] the BEs are ~36 (aug-cc-pVDZ/aug-cc-pVDZ) and ~49 (aug-cc-pVTZ/aug-cc- pVTZ) kJ.mol-1 (for details see Tables S1 in the supporting information). These are not very accurate values compared to those computed at the highest correlated level. But, 4 clearly demonstrate that even at the MC-HF level the system is bound and the computed BEs recover more than 65% (aug-cc-pVDZ/aug-cc-pVDZ) and 75% (aug-cc-pVTZ/aug- cc-pVTZ) of the exact BEs. This observation justifies employing the MC-HF wavefunction for further bonding analysis, as also used by CVR,[49] since the energetic origins of the binding must be present also at this computational level. The whole MC-QTAIM analysis was done using MC-HF/(aug-cc-pVTZ/aug-cc- pVTZ) wavefunction produced during the ab initio calculations. At first, the electronic, the positronic and the Gamma densities were produced.[52] The Gamma density for the positronic systems is simply the sum of the electronic and the positronic densities,[61–63] and is the basic scalar field used for the topological analysis and deducing the AIM boundaries within the context of the MC-QTAIM analysis. Figure 1 depicts these densities and the minus of the Laplacian of the positronic density, which acts like a magnifying glass, revealing the concentration and depletion of the positronic density. In line with the results reported by CVR the positronic density is concentrated in the middle of the two nuclei and depleted around each nucleus. The topological analysis of the Gamma density reveals two (3, -3) critical points (CPs) at the nuclei and a (3, -1) CP at the middle of the two nuclei. This topological structure, depicted in panel (e) of the figure, is the typical of diatomic molecules.[60] The concentration of the positronic density is not enough to shape a local maximum in the Gamma density at the middle of the two nuclei. Thus, the positron is not capable of forming its own atomic basin in this molecule (even adding a number of extra basis functions to the positronic basis set at the midpoint between the nuclei did not alter this pattern). As discussed recently in details,[71–73] not 5 the analysis of the topological structure nor the amounts of various property densities at (3, -1) CPs are safe grounds to decipher the nature of AIM interactions. Figure 1. The relief maps of (a) the positronic density, (b) the Laplacian of the positronic density, (c) the electronic density, and − + − (d) the Gamma density of H,, e H computed at the MC-HF/(aug-cc-pVTZ/aug-cc-pVTZ) level (the qualitative aspects of these plots are independent from the used basis sets). The red and black spheres in panel (d) are (3, -3) and (3, -1) CPs of the Gamma density, respectively, while the white thread is duo of gradient paths connecting (3, -3) CPs to (3, -1) CP.
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